<!doctype html>
<html>
<head>
<meta charset='UTF-8'><meta name='viewport' content='width=device-width initial-scale=1'>

<link href='https://fonts.loli.net/css?family=Open+Sans:400italic,700italic,700,400&subset=latin,latin-ext' rel='stylesheet' type='text/css' /><style type='text/css'>html {overflow-x: initial !important;}:root { --bg-color:#ffffff; --text-color:#333333; --select-text-bg-color:#B5D6FC; --select-text-font-color:auto; --monospace:"Lucida Console",Consolas,"Courier",monospace; --title-bar-height:20px; }
.mac-os-11 { --title-bar-height:28px; }
html { font-size: 14px; background-color: var(--bg-color); color: var(--text-color); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; -webkit-font-smoothing: antialiased; }
body { margin: 0px; padding: 0px; height: auto; bottom: 0px; top: 0px; left: 0px; right: 0px; font-size: 1rem; line-height: 1.42857; overflow-x: hidden; background: inherit; tab-size: 4; }
iframe { margin: auto; }
a.url { word-break: break-all; }
a:active, a:hover { outline: 0px; }
.in-text-selection, ::selection { text-shadow: none; background: var(--select-text-bg-color); color: var(--select-text-font-color); }
#write { margin: 0px auto; height: auto; width: inherit; word-break: normal; overflow-wrap: break-word; position: relative; white-space: normal; overflow-x: visible; padding-top: 36px; }
#write.first-line-indent p { text-indent: 2em; }
#write.first-line-indent li p, #write.first-line-indent p * { text-indent: 0px; }
#write.first-line-indent li { margin-left: 2em; }
.for-image #write { padding-left: 8px; padding-right: 8px; }
body.typora-export { padding-left: 30px; padding-right: 30px; }
.typora-export .footnote-line, .typora-export li, .typora-export p { white-space: pre-wrap; }
.typora-export .task-list-item input { pointer-events: none; }
@media screen and (max-width: 500px) {
  body.typora-export { padding-left: 0px; padding-right: 0px; }
  #write { padding-left: 20px; padding-right: 20px; }
  .CodeMirror-sizer { margin-left: 0px !important; }
  .CodeMirror-gutters { display: none !important; }
}
#write li > figure:last-child { margin-bottom: 0.5rem; }
#write ol, #write ul { position: relative; }
img { max-width: 100%; vertical-align: middle; image-orientation: from-image; }
button, input, select, textarea { color: inherit; font: inherit; }
input[type="checkbox"], input[type="radio"] { line-height: normal; padding: 0px; }
*, ::after, ::before { box-sizing: border-box; }
#write h1, #write h2, #write h3, #write h4, #write h5, #write h6, #write p, #write pre { width: inherit; }
#write h1, #write h2, #write h3, #write h4, #write h5, #write h6, #write p { position: relative; }
p { line-height: inherit; }
h1, h2, h3, h4, h5, h6 { break-after: avoid-page; break-inside: avoid; orphans: 4; }
p { orphans: 4; }
h1 { font-size: 2rem; }
h2 { font-size: 1.8rem; }
h3 { font-size: 1.6rem; }
h4 { font-size: 1.4rem; }
h5 { font-size: 1.2rem; }
h6 { font-size: 1rem; }
.md-math-block, .md-rawblock, h1, h2, h3, h4, h5, h6, p { margin-top: 1rem; margin-bottom: 1rem; }
.hidden { display: none; }
.md-blockmeta { color: rgb(204, 204, 204); font-weight: 700; font-style: italic; }
a { cursor: pointer; }
sup.md-footnote { padding: 2px 4px; background-color: rgba(238, 238, 238, 0.7); color: rgb(85, 85, 85); border-radius: 4px; cursor: pointer; }
sup.md-footnote a, sup.md-footnote a:hover { color: inherit; text-transform: inherit; text-decoration: inherit; }
#write input[type="checkbox"] { cursor: pointer; width: inherit; height: inherit; }
figure { overflow-x: auto; margin: 1.2em 0px; max-width: calc(100% + 16px); padding: 0px; }
figure > table { margin: 0px; }
tr { break-inside: avoid; break-after: auto; }
thead { display: table-header-group; }
table { border-collapse: collapse; border-spacing: 0px; width: 100%; overflow: auto; break-inside: auto; text-align: left; }
table.md-table td { min-width: 32px; }
.CodeMirror-gutters { border-right: 0px; background-color: inherit; }
.CodeMirror-linenumber { user-select: none; }
.CodeMirror { text-align: left; }
.CodeMirror-placeholder { opacity: 0.3; }
.CodeMirror pre { padding: 0px 4px; }
.CodeMirror-lines { padding: 0px; }
div.hr:focus { cursor: none; }
#write pre { white-space: pre-wrap; }
#write.fences-no-line-wrapping pre { white-space: pre; }
#write pre.ty-contain-cm { white-space: normal; }
.CodeMirror-gutters { margin-right: 4px; }
.md-fences { font-size: 0.9rem; display: block; break-inside: avoid; text-align: left; overflow: visible; white-space: pre; background: inherit; position: relative !important; }
.md-fences-adv-panel { width: 100%; margin-top: 10px; text-align: center; padding-top: 0px; padding-bottom: 8px; overflow-x: auto; }
#write .md-fences.mock-cm { white-space: pre-wrap; }
.md-fences.md-fences-with-lineno { padding-left: 0px; }
#write.fences-no-line-wrapping .md-fences.mock-cm { white-space: pre; overflow-x: auto; }
.md-fences.mock-cm.md-fences-with-lineno { padding-left: 8px; }
.CodeMirror-line, twitterwidget { break-inside: avoid; }
.footnotes { opacity: 0.8; font-size: 0.9rem; margin-top: 1em; margin-bottom: 1em; }
.footnotes + .footnotes { margin-top: 0px; }
.md-reset { margin: 0px; padding: 0px; border: 0px; outline: 0px; vertical-align: top; background: 0px 0px; text-decoration: none; text-shadow: none; float: none; position: static; width: auto; height: auto; white-space: nowrap; cursor: inherit; -webkit-tap-highlight-color: transparent; line-height: normal; font-weight: 400; text-align: left; box-sizing: content-box; direction: ltr; }
li div { padding-top: 0px; }
blockquote { margin: 1rem 0px; }
li .mathjax-block, li p { margin: 0.5rem 0px; }
li blockquote { margin: 1rem 0px; }
li { margin: 0px; position: relative; }
blockquote > :last-child { margin-bottom: 0px; }
blockquote > :first-child, li > :first-child { margin-top: 0px; }
.footnotes-area { color: rgb(136, 136, 136); margin-top: 0.714rem; padding-bottom: 0.143rem; white-space: normal; }
#write .footnote-line { white-space: pre-wrap; }
@media print {
  body, html { border: 1px solid transparent; height: 99%; break-after: avoid; break-before: avoid; font-variant-ligatures: no-common-ligatures; }
  #write { margin-top: 0px; padding-top: 0px; border-color: transparent !important; }
  .typora-export * { -webkit-print-color-adjust: exact; }
  .typora-export #write { break-after: avoid; }
  .typora-export #write::after { height: 0px; }
  .is-mac table { break-inside: avoid; }
  .typora-export-show-outline .typora-export-sidebar { display: none; }
}
.footnote-line { margin-top: 0.714em; font-size: 0.7em; }
a img, img a { cursor: pointer; }
pre.md-meta-block { font-size: 0.8rem; min-height: 0.8rem; white-space: pre-wrap; background: rgb(204, 204, 204); display: block; overflow-x: hidden; }
p > .md-image:only-child:not(.md-img-error) img, p > img:only-child { display: block; margin: auto; }
#write.first-line-indent p > .md-image:only-child:not(.md-img-error) img { left: -2em; position: relative; }
p > .md-image:only-child { display: inline-block; width: 100%; }
#write .MathJax_Display { margin: 0.8em 0px 0px; }
.md-math-block { width: 100%; }
.md-math-block:not(:empty)::after { display: none; }
.MathJax_ref { fill: currentcolor; }
[contenteditable="true"]:active, [contenteditable="true"]:focus, [contenteditable="false"]:active, [contenteditable="false"]:focus { outline: 0px; box-shadow: none; }
.md-task-list-item { position: relative; list-style-type: none; }
.task-list-item.md-task-list-item { padding-left: 0px; }
.md-task-list-item > input { position: absolute; top: 0px; left: 0px; margin-left: -1.2em; margin-top: calc(1em - 10px); border: none; }
.math { font-size: 1rem; }
.md-toc { min-height: 3.58rem; position: relative; font-size: 0.9rem; border-radius: 10px; }
.md-toc-content { position: relative; margin-left: 0px; }
.md-toc-content::after, .md-toc::after { display: none; }
.md-toc-item { display: block; color: rgb(65, 131, 196); }
.md-toc-item a { text-decoration: none; }
.md-toc-inner:hover { text-decoration: underline; }
.md-toc-inner { display: inline-block; cursor: pointer; }
.md-toc-h1 .md-toc-inner { margin-left: 0px; font-weight: 700; }
.md-toc-h2 .md-toc-inner { margin-left: 2em; }
.md-toc-h3 .md-toc-inner { margin-left: 4em; }
.md-toc-h4 .md-toc-inner { margin-left: 6em; }
.md-toc-h5 .md-toc-inner { margin-left: 8em; }
.md-toc-h6 .md-toc-inner { margin-left: 10em; }
@media screen and (max-width: 48em) {
  .md-toc-h3 .md-toc-inner { margin-left: 3.5em; }
  .md-toc-h4 .md-toc-inner { margin-left: 5em; }
  .md-toc-h5 .md-toc-inner { margin-left: 6.5em; }
  .md-toc-h6 .md-toc-inner { margin-left: 8em; }
}
a.md-toc-inner { font-size: inherit; font-style: inherit; font-weight: inherit; line-height: inherit; }
.footnote-line a:not(.reversefootnote) { color: inherit; }
.md-attr { display: none; }
.md-fn-count::after { content: "."; }
code, pre, samp, tt { font-family: var(--monospace); }
kbd { margin: 0px 0.1em; padding: 0.1em 0.6em; font-size: 0.8em; color: rgb(36, 39, 41); background: rgb(255, 255, 255); border: 1px solid rgb(173, 179, 185); border-radius: 3px; box-shadow: rgba(12, 13, 14, 0.2) 0px 1px 0px, rgb(255, 255, 255) 0px 0px 0px 2px inset; white-space: nowrap; vertical-align: middle; }
.md-comment { color: rgb(162, 127, 3); opacity: 0.8; font-family: var(--monospace); }
code { text-align: left; vertical-align: initial; }
a.md-print-anchor { white-space: pre !important; border-width: initial !important; border-style: none !important; border-color: initial !important; display: inline-block !important; position: absolute !important; width: 1px !important; right: 0px !important; outline: 0px !important; background: 0px 0px !important; text-decoration: initial !important; text-shadow: initial !important; }
.md-inline-math .MathJax_SVG .noError { display: none !important; }
.html-for-mac .inline-math-svg .MathJax_SVG { vertical-align: 0.2px; }
.md-fences-math .MathJax_SVG_Display, .md-math-block .MathJax_SVG_Display { text-align: center; margin: 0px; position: relative; text-indent: 0px; max-width: none; max-height: none; min-height: 0px; min-width: 100%; width: auto; overflow-y: visible; display: block !important; }
.MathJax_SVG_Display, .md-inline-math .MathJax_SVG_Display { width: auto; margin: inherit; display: inline-block !important; }
.MathJax_SVG .MJX-monospace { font-family: var(--monospace); }
.MathJax_SVG .MJX-sans-serif { font-family: sans-serif; }
.MathJax_SVG { display: inline; font-style: normal; font-weight: 400; line-height: normal; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; zoom: 90%; }
#math-inline-preview-content { zoom: 1.1; }
.MathJax_SVG * { transition: none 0s ease 0s; }
.MathJax_SVG_Display svg { vertical-align: middle !important; margin-bottom: 0px !important; margin-top: 0px !important; }
.os-windows.monocolor-emoji .md-emoji { font-family: "Segoe UI Symbol", sans-serif; }
.md-diagram-panel > svg { max-width: 100%; }
[lang="flow"] svg, [lang="mermaid"] svg { max-width: 100%; height: auto; }
[lang="mermaid"] .node text { font-size: 1rem; }
table tr th { border-bottom: 0px; }
video { max-width: 100%; display: block; margin: 0px auto; }
iframe { max-width: 100%; width: 100%; border: none; }
.highlight td, .highlight tr { border: 0px; }
mark { background: rgb(255, 255, 0); color: rgb(0, 0, 0); }
.md-html-inline .md-plain, .md-html-inline strong, mark .md-inline-math, mark strong { color: inherit; }
.md-expand mark .md-meta { opacity: 0.3 !important; }
mark .md-meta { color: rgb(0, 0, 0); }
@media print {
  .typora-export h1, .typora-export h2, .typora-export h3, .typora-export h4, .typora-export h5, .typora-export h6 { break-inside: avoid; }
}
.md-diagram-panel .messageText { stroke: none !important; }
.md-diagram-panel .start-state { fill: var(--node-fill); }
.md-diagram-panel .edgeLabel rect { opacity: 1 !important; }
.md-require-zoom-fix foreignobject { font-size: var(--mermaid-font-zoom); }
.md-fences.md-fences-math { font-size: 1em; }
.md-fences-math .MathJax_SVG_Display { margin-top: 8px; cursor: default; }
.md-fences-advanced:not(.md-focus) { padding: 0px; white-space: nowrap; border: 0px; }
.md-fences-advanced:not(.md-focus) { background: inherit; }
.typora-export-show-outline .typora-export-content { max-width: 1440px; margin: auto; display: flex; flex-direction: row; }
.typora-export-sidebar { width: 300px; font-size: 0.8rem; margin-top: 80px; margin-right: 18px; }
.typora-export-show-outline #write { --webkit-flex:2; flex: 2 1 0%; }
.typora-export-sidebar .outline-content { position: fixed; top: 0px; max-height: 100%; overflow: hidden auto; padding-bottom: 30px; padding-top: 60px; width: 300px; }
@media screen and (max-width: 1024px) {
  .typora-export-sidebar, .typora-export-sidebar .outline-content { width: 240px; }
}
@media screen and (max-width: 800px) {
  .typora-export-sidebar { display: none; }
}
.outline-content li, .outline-content ul { margin-left: 0px; margin-right: 0px; padding-left: 0px; padding-right: 0px; list-style: none; }
.outline-content ul { margin-top: 0px; margin-bottom: 0px; }
.outline-content strong { font-weight: 400; }
.outline-expander { width: 1rem; height: 1.42857rem; position: relative; display: table-cell; vertical-align: middle; cursor: pointer; padding-left: 4px; }
.outline-expander::before { content: ""; position: relative; font-family: Ionicons; display: inline-block; font-size: 8px; vertical-align: middle; }
.outline-item { padding-top: 3px; padding-bottom: 3px; cursor: pointer; }
.outline-expander:hover::before { content: ""; }
.outline-h1 > .outline-item { padding-left: 0px; }
.outline-h2 > .outline-item { padding-left: 1em; }
.outline-h3 > .outline-item { padding-left: 2em; }
.outline-h4 > .outline-item { padding-left: 3em; }
.outline-h5 > .outline-item { padding-left: 4em; }
.outline-h6 > .outline-item { padding-left: 5em; }
.outline-label { cursor: pointer; display: table-cell; vertical-align: middle; text-decoration: none; color: inherit; }
.outline-label:hover { text-decoration: underline; }
.outline-item:hover { border-color: rgb(245, 245, 245); background-color: var(--item-hover-bg-color); }
.outline-item:hover { margin-left: -28px; margin-right: -28px; border-left: 28px solid transparent; border-right: 28px solid transparent; }
.outline-item-single .outline-expander::before, .outline-item-single .outline-expander:hover::before { display: none; }
.outline-item-open > .outline-item > .outline-expander::before { content: ""; }
.outline-children { display: none; }
.info-panel-tab-wrapper { display: none; }
.outline-item-open > .outline-children { display: block; }
.typora-export .outline-item { padding-top: 1px; padding-bottom: 1px; }
.typora-export .outline-item:hover { margin-right: -8px; border-right: 8px solid transparent; }
.typora-export .outline-expander::before { content: "+"; font-family: inherit; top: -1px; }
.typora-export .outline-expander:hover::before, .typora-export .outline-item-open > .outline-item > .outline-expander::before { content: "−"; }
.typora-export-collapse-outline .outline-children { display: none; }
.typora-export-collapse-outline .outline-item-open > .outline-children, .typora-export-no-collapse-outline .outline-children { display: block; }
.typora-export-no-collapse-outline .outline-expander::before { content: "" !important; }
.typora-export-show-outline .outline-item-active > .outline-item .outline-label { font-weight: 700; }


.CodeMirror { height: auto; }
.CodeMirror.cm-s-inner { background: inherit; }
.CodeMirror-scroll { overflow: auto hidden; z-index: 3; }
.CodeMirror-gutter-filler, .CodeMirror-scrollbar-filler { background-color: rgb(255, 255, 255); }
.CodeMirror-gutters { border-right: 1px solid rgb(221, 221, 221); background: inherit; white-space: nowrap; }
.CodeMirror-linenumber { padding: 0px 3px 0px 5px; text-align: right; color: rgb(153, 153, 153); }
.cm-s-inner .cm-keyword { color: rgb(119, 0, 136); }
.cm-s-inner .cm-atom, .cm-s-inner.cm-atom { color: rgb(34, 17, 153); }
.cm-s-inner .cm-number { color: rgb(17, 102, 68); }
.cm-s-inner .cm-def { color: rgb(0, 0, 255); }
.cm-s-inner .cm-variable { color: rgb(0, 0, 0); }
.cm-s-inner .cm-variable-2 { color: rgb(0, 85, 170); }
.cm-s-inner .cm-variable-3 { color: rgb(0, 136, 85); }
.cm-s-inner .cm-string { color: rgb(170, 17, 17); }
.cm-s-inner .cm-property { color: rgb(0, 0, 0); }
.cm-s-inner .cm-operator { color: rgb(152, 26, 26); }
.cm-s-inner .cm-comment, .cm-s-inner.cm-comment { color: rgb(170, 85, 0); }
.cm-s-inner .cm-string-2 { color: rgb(255, 85, 0); }
.cm-s-inner .cm-meta { color: rgb(85, 85, 85); }
.cm-s-inner .cm-qualifier { color: rgb(85, 85, 85); }
.cm-s-inner .cm-builtin { color: rgb(51, 0, 170); }
.cm-s-inner .cm-bracket { color: rgb(153, 153, 119); }
.cm-s-inner .cm-tag { color: rgb(17, 119, 0); }
.cm-s-inner .cm-attribute { color: rgb(0, 0, 204); }
.cm-s-inner .cm-header, .cm-s-inner.cm-header { color: rgb(0, 0, 255); }
.cm-s-inner .cm-quote, .cm-s-inner.cm-quote { color: rgb(0, 153, 0); }
.cm-s-inner .cm-hr, .cm-s-inner.cm-hr { color: rgb(153, 153, 153); }
.cm-s-inner .cm-link, .cm-s-inner.cm-link { color: rgb(0, 0, 204); }
.cm-negative { color: rgb(221, 68, 68); }
.cm-positive { color: rgb(34, 153, 34); }
.cm-header, .cm-strong { font-weight: 700; }
.cm-del { text-decoration: line-through; }
.cm-em { font-style: italic; }
.cm-link { text-decoration: underline; }
.cm-error { color: red; }
.cm-invalidchar { color: red; }
.cm-constant { color: rgb(38, 139, 210); }
.cm-defined { color: rgb(181, 137, 0); }
div.CodeMirror span.CodeMirror-matchingbracket { color: rgb(0, 255, 0); }
div.CodeMirror span.CodeMirror-nonmatchingbracket { color: rgb(255, 34, 34); }
.cm-s-inner .CodeMirror-activeline-background { background: inherit; }
.CodeMirror { position: relative; overflow: hidden; }
.CodeMirror-scroll { height: 100%; outline: 0px; position: relative; box-sizing: content-box; background: inherit; }
.CodeMirror-sizer { position: relative; }
.CodeMirror-gutter-filler, .CodeMirror-hscrollbar, .CodeMirror-scrollbar-filler, .CodeMirror-vscrollbar { position: absolute; z-index: 6; display: none; }
.CodeMirror-vscrollbar { right: 0px; top: 0px; overflow: hidden; }
.CodeMirror-hscrollbar { bottom: 0px; left: 0px; overflow: hidden; }
.CodeMirror-scrollbar-filler { right: 0px; bottom: 0px; }
.CodeMirror-gutter-filler { left: 0px; bottom: 0px; }
.CodeMirror-gutters { position: absolute; left: 0px; top: 0px; padding-bottom: 30px; z-index: 3; }
.CodeMirror-gutter { white-space: normal; height: 100%; box-sizing: content-box; padding-bottom: 30px; margin-bottom: -32px; display: inline-block; }
.CodeMirror-gutter-wrapper { position: absolute; z-index: 4; background: 0px 0px !important; border: none !important; }
.CodeMirror-gutter-background { position: absolute; top: 0px; bottom: 0px; z-index: 4; }
.CodeMirror-gutter-elt { position: absolute; cursor: default; z-index: 4; }
.CodeMirror-lines { cursor: text; }
.CodeMirror pre { border-radius: 0px; border-width: 0px; background: 0px 0px; font-family: inherit; font-size: inherit; margin: 0px; white-space: pre; overflow-wrap: normal; color: inherit; z-index: 2; position: relative; overflow: visible; }
.CodeMirror-wrap pre { overflow-wrap: break-word; white-space: pre-wrap; word-break: normal; }
.CodeMirror-code pre { border-right: 30px solid transparent; width: fit-content; }
.CodeMirror-wrap .CodeMirror-code pre { border-right: none; width: auto; }
.CodeMirror-linebackground { position: absolute; left: 0px; right: 0px; top: 0px; bottom: 0px; z-index: 0; }
.CodeMirror-linewidget { position: relative; z-index: 2; overflow: auto; }
.CodeMirror-wrap .CodeMirror-scroll { overflow-x: hidden; }
.CodeMirror-measure { position: absolute; width: 100%; height: 0px; overflow: hidden; visibility: hidden; }
.CodeMirror-measure pre { position: static; }
.CodeMirror div.CodeMirror-cursor { position: absolute; visibility: hidden; border-right: none; width: 0px; }
.CodeMirror div.CodeMirror-cursor { visibility: hidden; }
.CodeMirror-focused div.CodeMirror-cursor { visibility: inherit; }
.cm-searching { background: rgba(255, 255, 0, 0.4); }
span.cm-underlined { text-decoration: underline; }
span.cm-strikethrough { text-decoration: line-through; }
.cm-tw-syntaxerror { color: rgb(255, 255, 255); background-color: rgb(153, 0, 0); }
.cm-tw-deleted { text-decoration: line-through; }
.cm-tw-header5 { font-weight: 700; }
.cm-tw-listitem:first-child { padding-left: 10px; }
.cm-tw-box { border-style: solid; border-right-width: 1px; border-bottom-width: 1px; border-left-width: 1px; border-color: inherit; border-top-width: 0px !important; }
.cm-tw-underline { text-decoration: underline; }
@media print {
  .CodeMirror div.CodeMirror-cursor { visibility: hidden; }
}


:root {
    --side-bar-bg-color: #fafafa;
    --control-text-color: #777;
}

@include-when-export url(https://fonts.loli.net/css?family=Open+Sans:400italic,700italic,700,400&subset=latin,latin-ext);

/* open-sans-regular - latin-ext_latin */
  /* open-sans-italic - latin-ext_latin */
    /* open-sans-700 - latin-ext_latin */
    /* open-sans-700italic - latin-ext_latin */
  html {
    font-size: 16px;
}

body {
    font-family: "Open Sans","Clear Sans", "Helvetica Neue", Helvetica, Arial, sans-serif;
    color: rgb(51, 51, 51);
    line-height: 1.6;
}

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<div id='write'  class=''><h1 id='强化学习原理与python实现更新与勘误'><span>《强化学习：原理与Python实现》更新与勘误</span></h1><p><span>（2019年12月第1版第3次印刷）</span></p><h3 id='行数计算方法'><span>行数计算方法</span></h3><p><span>本勘误文档中，行数计算“第</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.801ex" height="1.994ex" viewBox="0 -755.9 345 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="0" id="E100-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E100-MJMATHI-69" x="0" y="0"></use></g></svg></span><script type="math/tex">i</script><span>行”（</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="13.203ex" height="2.344ex" viewBox="0 -755.9 5684.6 1009.2" role="img" focusable="false" style="vertical-align: -0.588ex;"><defs><path stroke-width="0" id="E101-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path><path stroke-width="0" id="E101-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E101-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="0" id="E101-MJMAIN-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path stroke-width="0" id="E101-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E101-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path stroke-width="0" id="E101-MJMAIN-2026" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E101-MJMATHI-69" x="0" y="0"></use><use xlink:href="#E101-MJMAIN-3D" x="622" y="0"></use><use xlink:href="#E101-MJMAIN-30" x="1678" y="0"></use><use xlink:href="#E101-MJMAIN-2C" x="2178" y="0"></use><use xlink:href="#E101-MJMAIN-31" x="2623" y="0"></use><use xlink:href="#E101-MJMAIN-2C" x="3123" y="0"></use><use xlink:href="#E101-MJMAIN-32" x="3567" y="0"></use><use xlink:href="#E101-MJMAIN-2C" x="4067" y="0"></use><use xlink:href="#E101-MJMAIN-2026" x="4512" y="0"></use></g></svg></span><script type="math/tex">i=0,1,2,\ldots</script><span>）是从0开始计数的。小节标题、公式、内联代码、注意、本章要点记入行数，章标题、图、表、代码清单及它们的题注不计入行数。空行不计入行数。</span></p><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0" height="0.243ex" viewBox="0 -52.3 0 104.5" role="img" focusable="false" style="vertical-align: -0.121ex;"><defs></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"></g></svg></span><script type="math/tex">
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</script></p><h2 id='第17页第6行'><span>第17页第6行</span></h2><p><span>作者注：</span>
<span>“轨道”又称为“轨迹”。本书中这两个词混用。</span></p><h2 id='第20页第2行'><span>第20页第2行</span></h2><p><span>作者注：</span>
<span>这种带折扣的回报定义既可以用于回合制任务，也可以用于连续性任务，是一种统一的表示。</span></p><h2 id='第20页第9行'><span>第20页第9行</span></h2><p><span>为</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="23.048ex" height="6.079ex" viewBox="0 -1560 9923.2 2617.5" role="img" focusable="false" style="vertical-align: -2.456ex;"><defs><path stroke-width="0" id="E103-MJMATHI-52" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 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type="math/tex">\Delta=\left(1-\gamma\right)\left(1-\left(1-\alpha{x}-\beta{y}\right)\gamma\right)>0</script></p><h2 id='第28页第1行'><span>第28页第1行</span></h2><p><span>分母部分</span></p><h3 id='改为-3'><span>改为</span></h3><p><span>分子部分</span></p><h2 id='第30页'><span>第30页</span></h2><p><span>作者注：用线性规划求解最优状态价值的详细证明可见《Markov Decision Processes: Discrete Stochastic Dynamic Programming》（Martin Puterman）的第6.9节。证明大致如下：当</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.212ex" height="2.577ex" viewBox="0 -806.1 1813.7 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="0" id="E109-MJMATHI-63" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path stroke-width="0" id="E109-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path stroke-width="0" id="E109-MJSSI-73" d="M99 299Q99 318 106 341T133 393T195 441T298 461Q336 461 370 453T420 437L436 429Q436 428 421 389T405 350Q356 386 273 386H265Q248 386 237 384T211 371T191 337Q189 329 189 326Q189 320 190 315T194 306T200 299T209 293T218 289T228 285T239 283T251 281T263 278L270 276Q278 275 283 274T298 270T316 264T333 255T351 243T367 228T380 209T388 186T391 157Q391 96 341 43T193 -11Q171 -11 150 -8T114 -1T84 9T61 19T45 28T35 33Q35 36 67 116L76 109Q132 67 211 67Q258 67 279 88T301 135Q301 159 280 170T224 187T180 197Q141 212 120 239T99 299Z"></path><path stroke-width="0" id="E109-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E109-MJMATHI-63" x="0" y="0"></use><g transform="translate(599,0)"><use xlink:href="#E109-MJMAIN-28" x="0" y="0"></use><use xlink:href="#E109-MJSSI-73" x="389" y="0"></use><use xlink:href="#E109-MJMAIN-29" x="825" y="0"></use></g></g></svg></span><script type="math/tex">c\left(\sfs\right)</script><span>为Markov决策过程的初始状态分布时，原问题和对偶问题的目标都是Markov决策过程的平均回合奖励，原问题的最优解是最优状态价值。对</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.212ex" height="2.577ex" viewBox="0 -806.1 1813.7 1109.7" role="img" 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y="0"></use></g></g></svg></span><script type="math/tex">c\left(\sfs\right)</script><span>做灵敏度分析可知，无论</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.212ex" height="2.577ex" viewBox="0 -806.1 1813.7 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="0" id="E109-MJMATHI-63" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path stroke-width="0" id="E109-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 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stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E109-MJMATHI-63" x="0" y="0"></use><g transform="translate(599,0)"><use xlink:href="#E109-MJMAIN-28" x="0" y="0"></use><use xlink:href="#E109-MJSSI-73" x="389" y="0"></use><use xlink:href="#E109-MJMAIN-29" x="825" y="0"></use></g></g></svg></span><script type="math/tex">c\left(\sfs\right)</script><span>取什么分布，对偶问题均有解（这利用到对偶问题的可行域就是带折扣的状态动作对组成的分布所在的空间），所以原问题的最优解都是不变的。也就是说，Markov决策过程的最优状态价值和初始状态分布无关。进一步，可以在原问题中放宽</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.259ex" height="2.694ex" viewBox="0 -806.1 5278.2 1160" role="img" focusable="false" style="vertical-align: -0.822ex;"><defs><path stroke-width="0" id="E110-MJSZ1-2211" d="M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z"></path><path stroke-width="0" id="E110-MJSSI-73" d="M99 299Q99 318 106 341T133 393T195 441T298 461Q336 461 370 453T420 437L436 429Q436 428 421 389T405 350Q356 386 273 386H265Q248 386 237 384T211 371T191 337Q189 329 189 326Q189 320 190 315T194 306T200 299T209 293T218 289T228 285T239 283T251 281T263 278L270 276Q278 275 283 274T298 270T316 264T333 255T351 243T367 228T380 209T388 186T391 157Q391 96 341 43T193 -11Q171 -11 150 -8T114 -1T84 9T61 19T45 28T35 33Q35 36 67 116L76 109Q132 67 211 67Q258 67 279 88T301 135Q301 159 280 170T224 187T180 197Q141 212 120 239T99 299Z"></path><path stroke-width="0" id="E110-MJMATHI-63" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 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xlink:href="#E110-MJMAIN-31" x="4778" y="0"></use></g></svg></span><script type="math/tex">\sum\nolimits_{\sfs}c\left(\sfs\right)=1</script><span>这个限制，原问题的解依然不变，只是优化目标进行了放缩。</span></p><h2 id='第34页第9行'><span>第34页第9行</span></h2><p><span>计算这个动态规划问题</span></p><h3 id='改为-4'><span>改为</span></h3><p><span>计算这个线性规划问题</span></p><h2 id='第39页第1行'><span>第39页第1行</span></h2><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.108ex" height="2.694ex" viewBox="0 -856.4 2629.6 1160" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="0" id="E111-MJMATHI-76" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path stroke-width="0" id="E111-MJMAIN-2217" d="M229 286Q216 420 216 436Q216 454 240 464Q241 464 245 464T251 465Q263 464 273 456T283 436Q283 419 277 356T270 286L328 328Q384 369 389 372T399 375Q412 375 423 365T435 338Q435 325 425 315Q420 312 357 282T289 250L355 219L425 184Q434 175 434 161Q434 146 425 136T401 125Q393 125 383 131T328 171L270 213Q283 79 283 63Q283 53 276 44T250 35Q231 35 224 44T216 63Q216 80 222 143T229 213L171 171Q115 130 110 127Q106 124 100 124Q87 124 76 134T64 161Q64 166 64 169T67 175T72 181T81 188T94 195T113 204T138 215T170 230T210 250L74 315Q65 324 65 338Q65 353 74 363T98 374Q106 374 116 368T171 328L229 286Z"></path><path stroke-width="0" id="E111-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 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height="2.694ex" viewBox="0 -856.4 2176.1 1160" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="0" id="E112-MJMATHI-76" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path stroke-width="0" id="E112-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path stroke-width="0" id="E112-MJSSI-73" d="M99 299Q99 318 106 341T133 393T195 441T298 461Q336 461 370 453T420 437L436 429Q436 428 421 389T405 350Q356 386 273 386H265Q248 386 237 384T211 371T191 337Q189 329 189 326Q189 320 190 315T194 306T200 299T209 293T218 289T228 285T239 283T251 281T263 278L270 276Q278 275 283 274T298 270T316 264T333 255T351 243T367 228T380 209T388 186T391 157Q391 96 341 43T193 -11Q171 -11 150 -8T114 -1T84 9T61 19T45 28T35 33Q35 36 67 116L76 109Q132 67 211 67Q258 67 279 88T301 135Q301 159 280 170T224 187T180 197Q141 212 120 239T99 299Z"></path><path stroke-width="0" id="E112-MJMAIN-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path stroke-width="0" id="E112-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E112-MJMATHI-76" x="0" y="0"></use><g transform="translate(651,0)"><use xlink:href="#E112-MJMAIN-28"></use><g transform="translate(389,0)"><use xlink:href="#E112-MJSSI-73" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E112-MJMAIN-2032" x="639" y="513"></use></g><use xlink:href="#E112-MJMAIN-29" x="1135" y="0"></use></g></g></svg></span><script type="math/tex">v\left(\sfs'\right)</script></p><h2 id='第39页第25行'><span>第39页第25行</span></h2><p><span>（fix point）</span></p><h3 id='改为-6'><span>改为</span></h3><p><span>（fixed point）</span></p><h2 id='第42页第9行'><span>第42页第9行</span></h2><p><span>对于两个确定性的策略</span></p><h3 id='改为-7'><span>改为</span></h3><p><span>对于策略</span></p><h2 id='第56页第10行'><span>第56页第10行</span></h2><p><span>同时满足</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="18.251ex" height="2.577ex" viewBox="0 -806.1 7857.8 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="0" id="E114-MJMAIN-7B" d="M434 -231Q434 -244 428 -250H410Q281 -250 230 -184Q225 -177 222 -172T217 -161T213 -148T211 -133T210 -111T209 -84T209 -47T209 0Q209 21 209 53Q208 142 204 153Q203 154 203 155Q189 191 153 211T82 231Q71 231 68 234T65 250T68 266T82 269Q116 269 152 289T203 345Q208 356 208 377T209 529V579Q209 634 215 656T244 698Q270 724 324 740Q361 748 377 749Q379 749 390 749T408 750H428Q434 744 434 732Q434 719 431 716Q429 713 415 713Q362 710 332 689T296 647Q291 634 291 499V417Q291 370 288 353T271 314Q240 271 184 255L170 250L184 245Q202 239 220 230T262 196T290 137Q291 131 291 1Q291 -134 296 -147Q306 -174 339 -192T415 -213Q429 -213 431 -216Q434 -219 434 -231Z"></path><path stroke-width="0" id="E114-MJMATHI-3B1" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 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130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path stroke-width="0" id="E114-MJMAIN-3A" d="M78 370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 327T78 370ZM78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path stroke-width="0" id="E114-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E114-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 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xlink:href="#E114-MJMATHI-6B" x="905" y="-213"></use></g><use xlink:href="#E114-MJMAIN-3A" x="1886" y="0"></use><use xlink:href="#E114-MJMATHI-6B" x="2441" y="0"></use><use xlink:href="#E114-MJMAIN-3D" x="3240" y="0"></use><use xlink:href="#E114-MJMAIN-31" x="4296" y="0"></use><use xlink:href="#E114-MJMAIN-2C" x="4796" y="0"></use><use xlink:href="#E114-MJMAIN-32" x="5241" y="0"></use><use xlink:href="#E114-MJMAIN-2C" x="5741" y="0"></use><use xlink:href="#E114-MJMAIN-2026" x="6185" y="0"></use><use xlink:href="#E114-MJMAIN-7D" x="7357" y="0"></use></g></svg></span><script type="math/tex">\left\{\alpha_k:k=1,2,\ldots\right\}</script></p><h3 id='改为-8'><span>改为</span></h3><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="18.251ex" height="2.577ex" viewBox="0 -806.1 7857.8 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="0" id="E114-MJMAIN-7B" d="M434 -231Q434 -244 428 -250H410Q281 -250 230 -184Q225 -177 222 -172T217 -161T213 -148T211 -133T210 -111T209 -84T209 -47T209 0Q209 21 209 53Q208 142 204 153Q203 154 203 155Q189 191 153 211T82 231Q71 231 68 234T65 250T68 266T82 269Q116 269 152 289T203 345Q208 356 208 377T209 529V579Q209 634 215 656T244 698Q270 724 324 740Q361 748 377 749Q379 749 390 749T408 750H428Q434 744 434 732Q434 719 431 716Q429 713 415 713Q362 710 332 689T296 647Q291 634 291 499V417Q291 370 288 353T271 314Q240 271 184 255L170 250L184 245Q202 239 220 230T262 196T290 137Q291 131 291 1Q291 -134 296 -147Q306 -174 339 -192T415 -213Q429 -213 431 -216Q434 -219 434 -231Z"></path><path stroke-width="0" id="E114-MJMATHI-3B1" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 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xlink:href="#E114-MJMAIN-31" x="4296" y="0"></use><use xlink:href="#E114-MJMAIN-2C" x="4796" y="0"></use><use xlink:href="#E114-MJMAIN-32" x="5241" y="0"></use><use xlink:href="#E114-MJMAIN-2C" x="5741" y="0"></use><use xlink:href="#E114-MJMAIN-2026" x="6185" y="0"></use><use xlink:href="#E114-MJMAIN-7D" x="7357" y="0"></use></g></svg></span><script type="math/tex">\left\{\alpha_k:k=1,2,\ldots\right\}</script><span>同时满足</span></p><h2 id='第58页最后一行'><span>第58页最后一行</span></h2><p><span>态</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.788ex" height="2.11ex" viewBox="0 -554.9 1630.8 908.7" role="img" focusable="false" style="vertical-align: -0.822ex;"><defs><path stroke-width="0" id="E115-MJSSI-73" d="M99 299Q99 318 106 341T133 393T195 441T298 461Q336 461 370 453T420 437L436 429Q436 428 421 389T405 350Q356 386 273 386H265Q248 386 237 384T211 371T191 337Q189 329 189 326Q189 320 190 315T194 306T200 299T209 293T218 289T228 285T239 283T251 281T263 278L270 276Q278 275 283 274T298 270T316 264T333 255T351 243T367 228T380 209T388 186T391 157Q391 96 341 43T193 -11Q171 -11 150 -8T114 -1T84 9T61 19T45 28T35 33Q35 36 67 116L76 109Q132 67 211 67Q258 67 279 88T301 135Q301 159 280 170T224 187T180 197Q141 212 120 239T99 299Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E115-MJSSI-73" x="0" y="0"></use><g transform="translate(383,-156)"><text font-family="STIXGeneral, 'PingFang SC', serif" stroke="none" transform="scale(35.539) matrix(1 0 0 -1 0 0)">起</text><g transform="translate(579,0)"><text font-family="STIXGeneral, 'PingFang SC', serif" stroke="none" transform="scale(35.539) matrix(1 0 0 -1 0 0)">始</text></g></g></g></svg></span><script type="math/tex">\sfs_{起始}</script></p><h4 id='改为-9'><span>改为</span></h4><p><span>态</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.788ex" height="2.11ex" viewBox="0 -554.9 1630.8 908.7" role="img" focusable="false" style="vertical-align: -0.822ex;"><defs><path stroke-width="0" id="E116-MJSSI-73" d="M99 299Q99 318 106 341T133 393T195 441T298 461Q336 461 370 453T420 437L436 429Q436 428 421 389T405 350Q356 386 273 386H265Q248 386 237 384T211 371T191 337Q189 329 189 326Q189 320 190 315T194 306T200 299T209 293T218 289T228 285T239 283T251 281T263 278L270 276Q278 275 283 274T298 270T316 264T333 255T351 243T367 228T380 209T388 186T391 157Q391 96 341 43T193 -11Q171 -11 150 -8T114 -1T84 9T61 19T45 28T35 33Q35 36 67 116L76 109Q132 67 211 67Q258 67 279 88T301 135Q301 159 280 170T224 187T180 197Q141 212 120 239T99 299Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E116-MJSSI-73" x="0" y="0"></use><g transform="translate(383,-156)"><text font-family="STIXGeneral, 'PingFang SC', serif" stroke="none" transform="scale(35.539) matrix(1 0 0 -1 0 0)">开</text><g transform="translate(579,0)"><text font-family="STIXGeneral, 'PingFang SC', serif" stroke="none" transform="scale(35.539) matrix(1 0 0 -1 0 0)">始</text></g></g></g></svg></span><script type="math/tex">\sfs_{开始}</script></p><h2 id='第67页第3行'><span>第67页第3行</span></h2><p><span>范围为3~21的int型数值</span></p><h3 id='改为-10'><span>改为</span></h3><p><span>范围为4~21的int型数值</span></p><h2 id='第72页434节正文第1行第73页正文第0行'><span>第72页4.3.4节正文第1行，第73页正文第0行</span></h2><p><code>evaluate_action_monte_carlo_importance_resample</code></p><h3 id='改为-11'><span>改为</span></h3><p><code>evaluate_monte_carlo_importance_sample</code></p><h2 id='第72页代码清单4-7第0行第73页正文第7行'><span>第72页代码清单4-7第0行，第73页正文第7行</span></h2><p><code>evaluate_monte_carlo_importance_resample</code></p><h3 id='改为-12'><span>改为</span></h3><p><code>evaluate_monte_carlo_importance_sample</code></p><h2 id='第73页代码清单4-8第0行第74页正文第0行第74页正文第3行'><span>第73页代码清单4-8第0行，第74页正文第0行，第74页正文第3行</span></h2><p><code>monte_carlo_importance_resample</code></p><p><span>改为</span></p><p><code>monte_carlo_importance_sample</code></p><h2 id='第85页算法5-10输入'><span>第85页算法5-10输入</span></h2><p><span>输入：环境（无数学描述）、策略</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.331ex" height="1.41ex" viewBox="0 -504.6 573 607.1" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="0" id="E118-MJMATHI-3C0" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E118-MJMATHI-3C0" x="0" y="0"></use></g></svg></span><script type="math/tex">\pi</script><span>。</span></p><h4 id='改为-13'><span>改为</span></h4><p><span>输入：环境（无数学描述）、如果是策略评估还需要输入策略</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.331ex" height="1.41ex" viewBox="0 -504.6 573 607.1" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="0" id="E118-MJMATHI-3C0" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E118-MJMATHI-3C0" x="0" y="0"></use></g></svg></span><script type="math/tex">\pi</script><span>。</span></p><h2 id='第85页算法5-10第231步'><span>第85页算法5-10第2.3.1步</span></h2><p><span>根据</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.486ex" height="2.577ex" viewBox="0 -806.1 4514.9 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="0" id="E119-MJMATHI-3C0" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"></path><path stroke-width="0" id="E119-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path stroke-width="0" id="E119-MJMAIN-22C5" d="M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z"></path><path stroke-width="0" id="E119-MJMAIN-2223" d="M139 -249H137Q125 -249 119 -235V251L120 737Q130 750 139 750Q152 750 159 735V-235Q151 -249 141 -249H139Z"></path><path stroke-width="0" id="E119-MJSSI-53" d="M161 478Q161 568 242 642T435 716Q527 716 599 673L609 667Q595 633 589 615L571 568Q570 568 564 575T546 592T518 611T475 628T417 635Q351 635 305 596T259 507Q259 465 290 444T372 411T432 396Q473 385 509 343T545 236Q545 140 464 59T270 -22Q155 -22 54 48L92 146Q93 146 101 138T124 117T161 92T216 72T288 63Q360 63 403 109T447 204Q447 220 444 233T435 256T421 273T404 285T385 295T366 301T347 306T331 310T315 314T292 321T265 331T235 346T207 367T183 395T168 431T161 478Z"></path><path stroke-width="0" id="E119-MJMATHI-74" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path stroke-width="0" id="E119-MJMAIN-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path stroke-width="0" id="E119-MJMATHI-6E" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path stroke-width="0" id="E119-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E119-MJMATHI-3C0" x="0" y="0"></use><g transform="translate(739,0)"><use xlink:href="#E119-MJMAIN-28" x="0" y="0"></use><use xlink:href="#E119-MJMAIN-22C5" x="389" y="0"></use><use xlink:href="#E119-MJMAIN-2223" x="944" y="0"></use><g transform="translate(1500,0)"><use xlink:href="#E119-MJSSI-53" x="0" y="0"></use><g transform="translate(556,-150)"><use transform="scale(0.707)" xlink:href="#E119-MJMATHI-74" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E119-MJMAIN-2B" x="361" y="0"></use><use transform="scale(0.707)" xlink:href="#E119-MJMATHI-6E" x="1139" y="0"></use></g></g><use xlink:href="#E119-MJMAIN-29" x="3386" y="0"></use></g></g></svg></span><script type="math/tex">\pi\left(\cdot\mid\sfS_{t+n}\right)</script><span>决定</span></p><h4 id='改为-14'><span>改为</span></h4><p><span>根据</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.152ex" height="2.577ex" viewBox="0 -806.1 4370.9 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="0" id="E120-MJMATHI-62" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path><path stroke-width="0" id="E120-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 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32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path stroke-width="0" id="E120-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E120-MJMATHI-62" x="0" y="0"></use><g transform="translate(595,0)"><use xlink:href="#E120-MJMAIN-28" x="0" y="0"></use><use xlink:href="#E120-MJMAIN-22C5" x="389" y="0"></use><use xlink:href="#E120-MJMAIN-2223" x="944" y="0"></use><g transform="translate(1500,0)"><use xlink:href="#E120-MJSSI-53" x="0" y="0"></use><g transform="translate(556,-150)"><use transform="scale(0.707)" xlink:href="#E120-MJMATHI-74" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E120-MJMAIN-2B" x="361" y="0"></use><use transform="scale(0.707)" xlink:href="#E120-MJMATHI-6E" x="1139" y="0"></use></g></g><use xlink:href="#E120-MJMAIN-29" x="3386" y="0"></use></g></g></svg></span><script type="math/tex">b\left(\cdot\mid\sfS_{t+n}\right)</script><span>决定</span></p><h2 id='第91页算法5-13参数部分第92页算法5-14参数部分'><span>第91页算法5-13参数部分、第92页算法5-14参数部分</span></h2><p><span>参数：资格迹参数</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.331ex" height="2.461ex" viewBox="0 -806.1 573 1059.4" role="img" focusable="false" style="vertical-align: -0.588ex;"><defs><path stroke-width="0" id="E123-MJMATHI-3B2" d="M29 -194Q23 -188 23 -186Q23 -183 102 134T186 465Q208 533 243 584T309 658Q365 705 429 705H431Q493 705 533 667T573 570Q573 465 469 396L482 383Q533 332 533 252Q533 139 448 65T257 -10Q227 -10 203 -2T165 17T143 40T131 59T126 65L62 -188Q60 -194 42 -194H29ZM353 431Q392 431 427 419L432 422Q436 426 439 429T449 439T461 453T472 471T484 495T493 524T501 560Q503 569 503 593Q503 611 502 616Q487 667 426 667Q384 667 347 643T286 582T247 514T224 455Q219 439 186 308T152 168Q151 163 151 147Q151 99 173 68Q204 26 260 26Q302 26 349 51T425 137Q441 171 449 214T457 279Q457 337 422 372Q380 358 347 358H337Q258 358 258 389Q258 396 261 403Q275 431 353 431Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E123-MJMATHI-3B2" x="0" y="0"></use></g></svg></span><script type="math/tex">\beta</script><span>、</span></p><h4 id='改为-15'><span>改为</span></h4><p><span>参数：资格迹参数</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.354ex" height="1.994ex" viewBox="0 -755.9 583 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="0" id="E122-MJMATHI-3BB" d="M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E122-MJMATHI-3BB" x="0" y="0"></use></g></svg></span><script type="math/tex">\lambda</script><span>和</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.331ex" height="2.461ex" viewBox="0 -806.1 573 1059.4" role="img" focusable="false" style="vertical-align: -0.588ex;"><defs><path stroke-width="0" id="E123-MJMATHI-3B2" d="M29 -194Q23 -188 23 -186Q23 -183 102 134T186 465Q208 533 243 584T309 658Q365 705 429 705H431Q493 705 533 667T573 570Q573 465 469 396L482 383Q533 332 533 252Q533 139 448 65T257 -10Q227 -10 203 -2T165 17T143 40T131 59T126 65L62 -188Q60 -194 42 -194H29ZM353 431Q392 431 427 419L432 422Q436 426 439 429T449 439T461 453T472 471T484 495T493 524T501 560Q503 569 503 593Q503 611 502 616Q487 667 426 667Q384 667 347 643T286 582T247 514T224 455Q219 439 186 308T152 168Q151 163 151 147Q151 99 173 68Q204 26 260 26Q302 26 349 51T425 137Q441 171 449 214T457 279Q457 337 422 372Q380 358 347 358H337Q258 358 258 389Q258 396 261 403Q275 431 353 431Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E123-MJMATHI-3B2" x="0" y="0"></use></g></svg></span><script type="math/tex">\beta</script><span>、</span></p><h2 id='第91页算法5-13第235步'><span>第91页算法5-13第2.3.5步</span></h2><h3 id='改为-16'><span>改为</span></h3><p><span>2.2.5（更新价值）</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="57.647ex" height="2.577ex" viewBox="0 -806.1 24820.2 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="0" id="E124-MJMATHI-71" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 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type="math/tex">q\left(\sfs,\sfa\right)\leftarrow{q}\left(\sfs,\sfa\right)+\alpha{e}\left(\sfs,\sfa\right)\left[U-q\left(\sfS,\sfA\right)\right],\sfs\in\mathcal{S},\sfa\in\mathcal{A}\left(\sfs\right)</script><span>;</span></p><h2 id='第91页算法5-13第236步'><span>第91页算法5-13第2.3.6步</span></h2><p><span>退出2.2步</span></p><h4 id='改为-17'><span>改为</span></h4><p><span>退出2.3步</span></p><h2 id='第92页算法5-14第233步'><span>第92页算法5-14第2.3.3步</span></h2><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.235ex" height="2.461ex" viewBox="0 -806.1 5267.8 1059.4" role="img" focusable="false" style="vertical-align: -0.588ex;"><defs><path stroke-width="0" id="E125-MJSSI-73" d="M99 299Q99 318 106 341T133 393T195 441T298 461Q336 461 370 453T420 437L436 429Q436 428 421 389T405 350Q356 386 273 386H265Q248 386 237 384T211 371T191 337Q189 329 189 326Q189 320 190 315T194 306T200 299T209 293T218 289T228 285T239 283T251 281T263 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177 258Q172 247 164 239T151 227T136 218L127 213L124 202Q118 186 118 163Q120 124 165 86T292 48Q374 48 423 86T473 186V193Q473 267 347 327Q268 364 239 389Q191 431 191 486Q191 547 242 600T356 679T470 705Q472 705 478 705T489 704Q551 704 596 682T642 610Q642 566 621 545Q592 516 554 512Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E171-MJSSI-73" x="0" y="0"></use><use xlink:href="#E171-MJMAIN-2208" x="713" y="0"></use><use xlink:href="#E171-MJCAL-53" x="1658" y="0"></use></g></svg></span><script type="math/tex">\sfs\in\mathcal{S}</script></p><h2 id='第92页算法5-14第235步'><span>第92页算法5-14第2.3.5步</span></h2><h3 id='改为-19'><span>改为</span></h3><p><span>2.2.5（更新价值）</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="38.691ex" height="2.577ex" viewBox="0 -806.1 16658.7 1109.7" role="img" focusable="false" 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xlink:href="#E127-MJMAIN-2208" x="15071" y="0"></use><use xlink:href="#E127-MJCAL-53" x="16016" y="0"></use></g></svg></span><script type="math/tex">v\left(\sfs\right)\leftarrow{v}\left(\sfs\right)+\alpha{e}\left(\sfs\right)\left[U-v\left(\sfS\right)\right],\sfs\in\mathcal{S}</script><span>。</span></p><h2 id='第96页代码清单5-6第14行'><span>第96页代码清单5-6第14行</span></h2><pre class="md-fences md-end-block ty-contain-cm modeLoaded" spellcheck="false" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 9.33333px; left: 8px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"></textarea></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 0px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: 0px; width: 0px;"></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> &nbsp; &nbsp; &nbsp;  v = (self.q[next_state].sum() * self.epsilon + \</span></pre></div></div></div></div></div></div><div style="position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 23px;"></div><div class="CodeMirror-gutters" style="display: none; height: 23px;"></div></div></div></pre><h3 id='改为-20'><span>改为</span></h3><pre class="md-fences md-end-block ty-contain-cm modeLoaded" spellcheck="false" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 9.33333px; left: 8px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"></textarea></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 0px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: 0px; width: 0px;"></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> &nbsp; &nbsp; &nbsp;  v = (self.q[next_state].mean() * self.epsilon + \</span></pre></div></div></div></div></div></div><div style="position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 23px;"></div><div class="CodeMirror-gutters" style="display: none; height: 23px;"></div></div></div></pre><h2 id='第102页第12行'><span>第102页第12行</span></h2><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="21.998ex" height="3.278ex" viewBox="0 -1057.4 9471.5 1411.3" role="img" focusable="false" style="vertical-align: -0.822ex;"><defs><path stroke-width="0" id="E128-MJSZ1-2211" d="M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z"></path><path stroke-width="0" id="E128-MJMATHI-54" d="M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 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id='第118页'><span>第118页</span></h2><p><span>作者注：</span></p><p><span>砖瓦编码是一种历史悠久的特征构造方法，可用于回归、分类等问题。目前学术界倾向于用神经网络代替砖瓦编码来构造特征。由于砖瓦编码和强化学习没有直接关联，本书没有用过多的篇幅介绍砖瓦编码。</span></p><p><span>实际使用砖瓦编码时，不需要精确计算砖瓦的数量，常随意的大致估计砖瓦的数量作为特征数。如果设置的特征数大于真实的砖瓦数量，那么有些特征永远不会取到，有些浪费；如果设置的特征数小于真实的砖瓦数量，那么有多个砖瓦需要共享特征，具体逻辑可以见代码清单6-3中“冲突处理”部分。这些浪费和冲突往往不会造成明显的性能损失。</span></p><p><span>第118页砖瓦数计算：每个大网格的网格宽度刚好是整个取值范围的1/8。所以，第0层大网格每个维度有8个大网格；第1~7层由于有偏移，每个维度需要有9个大网格才能覆盖整个取值范围。第117页图6-3b的情况略有不同：这个图中每个维度的取值范围不是大网格的长度的整数倍。所以有些层偏移后，不需要更多的大网格也可以覆盖整个取值范围。</span></p><h2 id='第126页最后一行'><span>第126页最后一行</span></h2><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="26.786ex" height="4.328ex" viewBox="0 -806.1 11532.7 1863.6" role="img" focusable="false" style="vertical-align: -2.456ex;"><defs><path stroke-width="0" id="E131-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 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x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E136-MJMATHI-74" x="943" y="-213"></use></g><use xlink:href="#E136-MJMAIN-7C" x="1411" y="0"></use><g transform="translate(1689,0)"><use xlink:href="#E136-MJSSI-53" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E136-MJMATHI-74" x="786" y="-213"></use></g><use xlink:href="#E136-MJMAIN-3B" x="2600" y="0"></use><g transform="translate(3045,0)"><g><use xlink:href="#E136-MJMATHI-3B8" x="0" y="0"></use></g></g><use xlink:href="#E136-MJMATHI-3B8" x="3095" y="0"></use><use xlink:href="#E136-MJMAIN-29" x="3564" y="0"></use></g></g></svg></span><script type="math/tex">\alpha\gamma^tG_t\nabla\pi\left(\sfA_t|\sfS_t;\bftheta\right)</script></p><h2 id='第129页第15行'><span>第129页第15行</span></h2><p><span>随机变量</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="21.073ex" height="6.196ex" viewBox="0 -1610.3 9072.9 2667.7" role="img" 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38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E137-MJMATHI-42" x="0" y="0"></use><g transform="translate(925,0)"><use xlink:href="#E137-MJMAIN-28" x="0" y="0"></use><use xlink:href="#E137-MJSSI-53" x="389" y="0"></use><use xlink:href="#E137-MJMAIN-29" x="998" y="0"></use></g><use xlink:href="#E137-MJMAIN-3D" x="2590" y="0"></use><use xlink:href="#E137-MJMAIN-2212" x="3646" y="0"></use><g transform="translate(4590,0)"><use xlink:href="#E137-MJSZ1-2211" x="106" y="0"></use><g transform="translate(0,-888)"><use transform="scale(0.707)" 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transform="translate(0,-888)"><use transform="scale(0.707)" xlink:href="#E138-MJMATHI-3C4" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E138-MJMAIN-3D" x="517" y="0"></use><use transform="scale(0.707)" xlink:href="#E138-MJMAIN-30" x="1295" y="0"></use></g><g transform="translate(55,950)"><use transform="scale(0.707)" xlink:href="#E138-MJMATHI-74" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E138-MJMAIN-2212" x="361" y="0"></use><use transform="scale(0.707)" xlink:href="#E138-MJMAIN-31" x="1139" y="0"></use></g></g><g transform="translate(6026,0)"><use xlink:href="#E138-MJMATHI-3B3" x="0" y="0"></use><g transform="translate(550,362)"><use transform="scale(0.707)" xlink:href="#E138-MJMATHI-3C4" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E138-MJMAIN-2212" x="517" y="0"></use><use transform="scale(0.707)" xlink:href="#E138-MJMATHI-74" x="1295" y="0"></use></g></g><g transform="translate(7848,0)"><use xlink:href="#E138-MJMATHI-52" x="0" y="0"></use><g transform="translate(759,-150)"><use transform="scale(0.707)" xlink:href="#E138-MJMATHI-3C4" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E138-MJMAIN-2B" x="517" y="0"></use><use transform="scale(0.707)" xlink:href="#E138-MJMAIN-31" x="1295" y="0"></use></g></g></g></svg></span><script type="math/tex">B\left(\sfS\right)=-\sum\limits_{\tau=0}^{t-1}\gamma^{\tau-t}R_{\tau+1}</script><span>，</span></p><h2 id='第131页算法7-3第23步'><span>第131页算法7-3第2.3步</span></h2><p><span>2.3（初始化回报和权重）</span></p><h4 id='改为-26'><span>改为</span></h4><p><span>2.3（初始化回报）</span></p><h2 id='第137页代码清单7-1中learn函数'><span>第137页代码清单7-1中</span><code>learn()</code><span>函数</span></h2><pre class="md-fences md-end-block ty-contain-cm modeLoaded" spellcheck="false" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 9.33333px; left: 8px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"></textarea></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 0px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: 0px; width: 0px;"></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  y = np.eye(self.action_n)[df['action']] * \</span></pre></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  df['psi'].values[:, np.newaxis]</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  self.policy_net.fit(x, y, verbose=0)</span></pre></div></div></div></div></div><div style="position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 68px;"></div><div class="CodeMirror-gutters" style="display: none; height: 68px;"></div></div></div></pre><h4 id='改为-27'><span>改为</span></h4><pre class="md-fences md-end-block ty-contain-cm modeLoaded" spellcheck="false" lang=""><div class="CodeMirror cm-s-inner CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 9.33333px; left: 8px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"></textarea></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 0px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: 0px; width: 0px;"></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  sample_weight = df['psi'].values[:, np.newaxis]</span></pre></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  y = np.eye(self.action_n)[df['action']]</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  self.policy_net.fit(x, y, sample_weight=sample_weight, verbose=0)</span></pre></div></div></div></div></div><div style="position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 68px;"></div><div class="CodeMirror-gutters" style="display: none; height: 68px;"></div></div></div></pre><h2 id='第142页算法83第232步'><span>第142页算法8.3第2.3.2步</span></h2><p><span>作者注：这里的更新式子遵循了论文原文而没有考虑累积折扣。推导出现折扣是正确的；更新时考虑折扣也是正确和合理的。</span></p><h2 id='第143页第5行第143页算法84第234步共2处）'><span>第143页第5行，第143页算法8.4第2.3.4步（共2处）</span></h2><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="16.033ex" height="2.577ex" viewBox="0 -806.1 6903.2 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="0" id="E139-MJMAIN-2207" d="M46 676Q46 679 51 683H781Q786 679 786 676Q786 674 617 326T444 -26Q439 -33 416 -33T388 -26Q385 -22 216 326T46 676ZM697 596Q697 597 445 597T193 596Q195 591 319 336T445 80L697 596Z"></path><path stroke-width="0" id="E139-MJMAIN-6C" d="M42 46H56Q95 46 103 60V68Q103 77 103 91T103 124T104 167T104 217T104 272T104 329Q104 366 104 407T104 482T104 542T103 586T103 603Q100 622 89 628T44 637H26V660Q26 683 28 683L38 684Q48 685 67 686T104 688Q121 689 141 690T171 693T182 694H185V379Q185 62 186 60Q190 52 198 49Q219 46 247 46H263V0H255L232 1Q209 2 183 2T145 3T107 3T57 1L34 0H26V46H42Z"></path><path stroke-width="0" id="E139-MJMAIN-6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 431 27 431L37 432Q47 433 65 434T102 436Q119 437 138 438T167 441T178 442H181V402Q181 364 182 364T187 369T199 384T218 402T247 421T285 437Q305 442 336 442Q450 438 463 329Q464 322 464 190V104Q464 66 466 59T477 49Q498 46 526 46H542V0H534L510 1Q487 2 460 2T422 3Q319 3 310 0H302V46H318Q379 46 379 62Q380 64 380 200Q379 335 378 343Q372 371 358 385T334 402T308 404Q263 404 229 370Q202 343 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738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E139-MJMAIN-2207" x="0" y="0"></use><g transform="translate(999,0)"><use xlink:href="#E139-MJMAIN-6C"></use><use xlink:href="#E139-MJMAIN-6E" x="278" y="0"></use></g><use xlink:href="#E139-MJMATHI-3C0" x="2000" y="0"></use><g transform="translate(2739,0)"><use xlink:href="#E139-MJMAIN-28" x="0" y="0"></use><use xlink:href="#E139-MJSSI-41" x="389" y="0"></use><use xlink:href="#E139-MJMAIN-2223" x="1333" y="0"></use><use xlink:href="#E139-MJSSI-53" x="1889" y="0"></use><use xlink:href="#E139-MJMAIN-3B" x="2498" y="0"></use><use xlink:href="#E139-MJMAINB-77" x="2943" y="0"></use><use xlink:href="#E139-MJMAIN-29" x="3774" y="0"></use></g></g></svg></span><script type="math/tex">\nabla\ln\pi\left(\sfA\mid\sfS;\mathbf{w}\right)</script></p><p><span>改为</span></p><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="15.309ex" height="2.577ex" viewBox="0 -806.1 6591.5 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="0" id="E140-MJMAIN-2207" d="M46 676Q46 679 51 683H781Q786 679 786 676Q786 674 617 326T444 -26Q439 -33 416 -33T388 -26Q385 -22 216 326T46 676ZM697 596Q697 597 445 597T193 596Q195 591 319 336T445 80L697 596Z"></path><path stroke-width="0" id="E140-MJMAIN-6C" d="M42 46H56Q95 46 103 60V68Q103 77 103 91T103 124T104 167T104 217T104 272T104 329Q104 366 104 407T104 482T104 542T103 586T103 603Q100 622 89 628T44 637H26V660Q26 683 28 683L38 684Q48 685 67 686T104 688Q121 689 141 690T171 693T182 694H185V379Q185 62 186 60Q190 52 198 49Q219 46 247 46H263V0H255L232 1Q209 2 183 2T145 3T107 3T57 1L34 0H26V46H42Z"></path><path stroke-width="0" id="E140-MJMAIN-6E" d="M41 46H55Q94 46 102 60V68Q102 77 102 91T102 122T103 161T103 203Q103 234 103 269T102 328V351Q99 370 88 376T43 385H25V408Q25 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transform="translate(2943,0)"><g><use xlink:href="#E140-MJMATHI-3B8" x="0" y="0"></use></g></g><use xlink:href="#E140-MJMATHI-3B8" x="2993" y="0"></use><use xlink:href="#E140-MJMAIN-29" x="3462" y="0"></use></g></g></svg></span><script type="math/tex">\nabla\ln\pi\left(\sfA\mid\sfS;\bftheta\right)</script></p><h2 id='第144页第711行'><span>第144页第7~11行</span></h2><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="24.054ex" height="6.079ex" viewBox="0 -1560 10356.7 2617.5" role="img" focusable="false" style="vertical-align: -2.456ex;"><defs><path stroke-width="0" id="E141-MJMAIN-45" d="M128 619Q121 626 117 628T101 631T58 634H25V680H597V676Q599 670 611 560T625 444V440H585V444Q584 447 582 465Q578 500 570 526T553 571T528 601T498 619T457 629T411 633T353 634Q266 634 251 633T233 622Q233 622 233 621Q232 619 232 497V376H286Q359 378 377 385Q413 401 416 469Q416 471 416 473V493H456V213H416V233Q415 268 408 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transform="translate(1744,0)"><use xlink:href="#E152-MJSSI-41" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E152-MJMATHI-74" x="943" y="-213"></use></g><use xlink:href="#E152-MJMAIN-29" x="2767" y="0"></use></g><use xlink:href="#E152-MJSZ2-5D" x="5950" y="-1"></use></g></g></svg></span><script type="math/tex">\E_{\sfS_t,\sfA_t\sim\pi\left(\bftheta\right)}\left[a_{\pi_{\left(\bftheta_k\right)}}\left(\sfS_t,\sfA_t\right)\right]</script></p><h2 id='第146页算法8-5第23步'><span>第146页算法8-5第2.3步</span></h2><p><span>更新</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.206ex" height="2.11ex" viewBox="0 -806.1 519.3 908.7" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="0" id="E154-MJMATHI-3B8" d="M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 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495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g><use xlink:href="#E154-MJMATHI-3B8" x="0" y="0"></use></g><use xlink:href="#E154-MJMATHI-3B8" x="50" y="0"></use></g></svg></span><script type="math/tex">\bftheta</script><span>以增大</span></p><h2 id='第147页图8-1中间线的注记'><span>第147页图8-1中间线的注记</span></h2><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.089ex" height="2.811ex" viewBox="0 -755.9 1330 1210.2" role="img" focusable="false" style="vertical-align: -1.055ex;"><defs><path stroke-width="0" id="E155-MJMATHI-6C" d="M117 59Q117 26 142 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y="0"></use><use xlink:href="#E162-MJSSI-61" x="389" y="0"></use><use xlink:href="#E162-MJMAIN-2223" x="1147" y="0"></use><g transform="translate(1703,0)"><use xlink:href="#E162-MJSSI-53" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E162-MJMATHI-74" x="786" y="-213"></use></g><use xlink:href="#E162-MJMAIN-3B" x="2614" y="0"></use><g transform="translate(3059,0)"><g><use xlink:href="#E162-MJMATHI-3B8" x="0" y="0"></use></g></g><use xlink:href="#E162-MJMATHI-3B8" x="3109" y="0"></use><use xlink:href="#E162-MJMAIN-29" x="3578" y="0"></use></g><use xlink:href="#E162-MJMAIN-2E" x="14025" y="0"></use></g></svg></span><script type="math/tex">=-\sum\limits_\sfa\frac{\pi\left(\sfa\mid\sfS_t;\bftheta^\mathrm{EMA}\right)}{\pi\left(\sfa\mid\sfS_t;\bftheta\right)} {\nabla_{\bftheta}} \pi\left(\sfa\mid\sfS_t;\bftheta\right).</script></p><h2 id='第150页算法8-7第21步'><span>第150页算法8-7第2.1步</span></h2><p><span>2.1  </span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; 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254H48V262Z"></path><path stroke-width="0" id="E164-MJMAIN-2190" d="M944 261T944 250T929 230H165Q167 228 182 216T211 189T244 152T277 96T303 25Q308 7 308 0Q308 -11 288 -11Q281 -11 278 -11T272 -7T267 2T263 21Q245 94 195 151T73 236Q58 242 55 247Q55 254 59 257T73 264Q121 283 158 314T215 375T247 434T264 480L267 497Q269 503 270 505T275 509T288 511Q308 511 308 500Q308 493 303 475Q293 438 278 406T246 352T215 315T185 287T165 270H929Q944 261 944 250Z"></path><path stroke-width="0" id="E164-MJMAINB-46" d="M425 0L228 3Q63 3 51 0H39V62H147V618H39V680H644V676Q647 670 659 552T675 428V424H613Q613 433 605 477Q599 511 589 535T562 574T530 599T488 612T441 617T387 618H368H304V371H333Q389 373 411 390T437 468V488H499V192H437V212Q436 244 430 263T408 292T378 305T333 309H304V62H439V0H425Z"></path><path stroke-width="0" id="E164-MJMAINB-70" d="M32 442L123 446Q214 450 215 450H221V409Q222 409 229 413T251 423T284 436T328 446T382 450Q480 450 540 388T600 223Q600 128 539 61T361 -6H354Q292 -6 236 28L227 34V-132H296V-194H287Q269 -191 163 -191Q56 -191 38 -194H29V-132H98V113V284Q98 330 97 348T93 370T83 376Q69 380 42 380H29V442H32ZM457 224Q457 303 427 349T350 395Q282 395 235 352L227 345V104L233 97Q274 45 337 45Q383 45 420 86T457 224Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E164-MJMAINB-7A" x="0" y="0"></use><use xlink:href="#E164-MJMAIN-2190" x="788" y="0"></use><g transform="translate(2066,0)"><use xlink:href="#E164-MJMAINB-46" x="0" y="0"></use><use xlink:href="#E164-MJMAINB-70" x="724" y="0"></use></g></g></svg></span><script type="math/tex">\mathbf{z}\leftarrow\mathbf{Fp}</script></p><h3 id='第161页第45行'><span>第161页第4~5行</span></h3><p><span>作者注：“动作价值网络和策略网络往往采用矢量形式的输出”指的是动作空间是离散动作空间的情况。如果动作空间是连续动作空间，往往用Gaussian形式的策略，详见GitHub代码。包括SAC算法在内的使用策略梯度的算法采用Gaussian形式策略后，策略被限制为了单峰（unimodal）形式。如果需要策略具有多峰（multimodal）形式，可以使用混合Gaussian模型（Gaussian Mixture Model，GMM）。</span></p><h2 id='第161页86节'><span>第161页8.6节</span></h2><p><span>作者注：这个案例的动作空间是离散的。同时，本章介绍的算法，包括但不限于PPO、SAC等算法，也可用于动作空间是连续空间的情况。</span></p><h2 id='第162页第17行'><span>第162页第17行</span></h2><p><span>单5-7中的</span></p><h3 id='改为-36'><span>改为</span></h3><p><span>单5-3中的</span></p><h2 id='第165页代码清单8-2前4行中间有个空行不计入）'><span>第165页代码清单8-2前4行（中间有个空行不计入）</span></h2><p><span>多缩进4个空格</span></p><h2 id='第173页第9行'><span>第173页第9行</span></h2><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.71ex" height="2.928ex" viewBox="0 -806.1 4611.1 1260.5" role="img" focusable="false" style="vertical-align: -1.055ex;"><defs><path stroke-width="0" id="E165-MJMAIN-2207" d="M46 676Q46 679 51 683H781Q786 679 786 676Q786 674 617 326T444 -26Q439 -33 416 -33T388 -26Q385 -22 216 326T46 676ZM697 596Q697 597 445 597T193 596Q195 591 319 336T445 80L697 596Z"></path><path stroke-width="0" id="E165-MJMATHI-76" d="M173 380Q173 405 154 405Q130 405 104 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x="1174" y="0"></use><use transform="scale(0.707)" xlink:href="#E176-MJMAIN-29" x="1643" y="0"></use></g></g></g><use xlink:href="#E176-MJSZ2-5D" x="13518" y="-1"></use></g></g></svg></span><script type="math/tex">=\E_{\rho_{\pi\left(\bftheta\right)}}\left[\nabla\pi\left(\sfs;\bftheta\right)\left[\nabla_\sfa{q}_{\pi\left(\bftheta\right)}\left(\sfs,\sfa\right)\right]_{\sfa=\pi\left(\sfs;\bftheta\right)}\right]</script></p><h4 id='改为-40'><span>改为</span></h4><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="57.552ex" height="6.079ex" viewBox="0 -1560 24779.1 2617.5" role="img" focusable="false" style="vertical-align: -2.456ex;"><defs><path stroke-width="0" id="E177-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E177-MJSZ1-2211" d="M61 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y="0"></use><use transform="scale(0.707)" xlink:href="#E179-MJSSI-73" x="389" y="0"></use><use transform="scale(0.707)" xlink:href="#E179-MJMAIN-3B" x="825" y="0"></use><g transform="translate(779,0)"><g><use transform="scale(0.707)" xlink:href="#E179-MJMATHI-3B8" x="0" y="0"></use></g></g><use transform="scale(0.707)" xlink:href="#E179-MJMATHI-3B8" x="1174" y="0"></use><use transform="scale(0.707)" xlink:href="#E179-MJMAIN-29" x="1643" y="0"></use></g></g></g></g></svg></span><script type="math/tex">=\sum\limits_{\sfs}^{}\rho_{\pi\left(\bftheta\right)}\left(\sfs\right)\nabla\pi\left(\sfs;\bftheta\right)\left[\nabla_\sfa{q}_{\pi\left(\bftheta\right)}\right]_{\sfa=\pi\left(\sfs;\bftheta\right)}</script></p><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="41.478ex" height="4.445ex" viewBox="0 -1208.2 17858.5 1913.9" role="img" focusable="false" style="vertical-align: -1.639ex;"><defs><path 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transform="translate(7924,0)"><use xlink:href="#E182-MJMATHI-42" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E182-MJMATHI-3C4" x="1073" y="-213"></use></g><use xlink:href="#E182-MJSZ2-5D" x="9149" y="-1"></use></g></g></svg></span><script type="math/tex">\sigma^2e^{-\theta\left(t+s\right)}\E\left[\int_{0}^{t}e^{\theta\tau}\mathrm{d}B_\tau\int_{0}^{s}e^{\theta\tau}\mathrm{d}B_\tau\right]</script></p><h2 id='第176页到第177页92节正文'><span>第176页到第177页9.2节正文</span></h2><h3 id='改为-42'><span>改为</span></h3><p><span>对于连续的动作空间，我们希望能够找到一个确定性策略，使得每条轨迹的回报最大。同策确定性算法利用策略</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.731ex" height="2.577ex" viewBox="0 -806.1 2036.9 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="0" id="E190-MJMATHI-3C0" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 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type="math/tex">\pi\left(\bftheta\right)</script><span>生成轨迹，并在这些轨迹上求得回报的平均值，通过让平均回报最大，使得每条轨迹上的回报尽可能大。事实上，如果每条轨迹的回报都要最大，那么对于任意策略</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.996ex" height="1.994ex" viewBox="0 -755.9 429 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="0" id="E189-MJMATHI-62" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></defs><g stroke="currentColor" fill="currentColor" 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type="math/tex">\nabla\E_{\rho_b}\left[q_{\pi\left(\bftheta\right)}\left(\sfS,\pi\left(\sfS;\bftheta\right)\right)\right]=\E_{\rho_b}\left[\nabla\pi\left(\sfS;\bftheta\right)\left[\nabla_a{q}_{\pi\left(\bftheta\right)}\left(\sfS,\sfa\right)\right]_{\sfa=\pi\left(\sfS;\bftheta\right)}\right]</script><span>。这个表达式与同策的情形相比，期望运算针对的表达式相同。所以，异策确定性算法的迭代式与同策确定性算法的迭代式相同。</span></p><p><span>异策确定性算法可能比同策确定性算法性能好的原因在于，行为策略可能会促进探索，用行为策略采样得到的轨迹能够更加全面的探索轨迹空间。这时候，最大化对轨迹分布的平均期望时能够同时考虑到更多不同的轨迹，使得在整个轨迹空间上的所有轨迹的回报会更大。</span></p><p><span>与非确定性策略梯度相比，非确定性异策算法的迭代式中含有重采样因子</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="8.03ex" height="4.445ex" viewBox="0 -1208.2 3457.6 1913.9" role="img" focusable="false" style="vertical-align: -1.639ex;"><defs><path stroke-width="0" id="E188-MJMATHI-3C0" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 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x="3418" y="0"></use></g></g><g transform="translate(400,-435)"><use transform="scale(0.707)" xlink:href="#E188-MJMATHI-62" x="0" y="0"></use><g transform="translate(303,0)"><use transform="scale(0.707)" xlink:href="#E188-MJMAIN-28" x="0" y="0"></use><g transform="translate(275,0)"><use transform="scale(0.707)" xlink:href="#E188-MJSSI-41" x="0" y="0"></use><use transform="scale(0.5)" xlink:href="#E188-MJMATHI-74" x="943" y="-213"></use></g><use transform="scale(0.707)" xlink:href="#E188-MJMAIN-7C" x="1411" y="0"></use><g transform="translate(1194,0)"><use transform="scale(0.707)" xlink:href="#E188-MJSSI-53" x="0" y="0"></use><use transform="scale(0.5)" xlink:href="#E188-MJMATHI-74" x="786" y="-213"></use></g><use transform="scale(0.707)" xlink:href="#E188-MJMAIN-29" x="2600" y="0"></use></g></g></g></g></svg></span><script type="math/tex">\frac{\pi\left(\sfA_t|\sfS_t;\bftheta\right)}{b\left(\sfA_t|\sfS_t\right)}</script><span>，而确定性异策算法中没有。这是因为，确定性的行为策略</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.996ex" height="1.994ex" viewBox="0 -755.9 429 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="0" id="E189-MJMATHI-62" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E189-MJMATHI-62" x="0" y="0"></use></g></svg></span><script type="math/tex">b</script><span>并不对于确定性的目标策略</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.731ex" height="2.577ex" viewBox="0 -806.1 2036.9 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="0" id="E190-MJMATHI-3C0" d="M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z"></path><path stroke-width="0" id="E190-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 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442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path><path stroke-width="0" id="E191-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path stroke-width="0" id="E191-MJMAIN-22C5" d="M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z"></path><path stroke-width="0" id="E191-MJMAIN-2223" d="M139 -249H137Q125 -249 119 -235V251L120 737Q130 750 139 750Q152 750 159 735V-235Q151 -249 141 -249H139Z"></path><path stroke-width="0" id="E191-MJSSI-53" d="M161 478Q161 568 242 642T435 716Q527 716 599 673L609 667Q595 633 589 615L571 568Q570 568 564 575T546 592T518 611T475 628T417 635Q351 635 305 596T259 507Q259 465 290 444T372 411T432 396Q473 385 509 343T545 236Q545 140 464 59T270 -22Q155 -22 54 48L92 146Q93 146 101 138T124 117T161 92T216 72T288 63Q360 63 403 109T447 204Q447 220 444 233T435 256T421 273T404 285T385 295T366 301T347 306T331 310T315 314T292 321T265 331T235 346T207 367T183 395T168 431T161 478Z"></path><path stroke-width="0" id="E191-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E191-MJMATHI-62" x="0" y="0"></use><use xlink:href="#E191-MJMAIN-28" x="429" y="0"></use><use xlink:href="#E191-MJMAIN-22C5" x="818" y="0"></use><use xlink:href="#E191-MJMAIN-2223" x="1373" y="0"></use><use xlink:href="#E191-MJSSI-53" x="1929" y="0"></use><use xlink:href="#E191-MJMAIN-29" x="2538" y="0"></use></g></svg></span><script type="math/tex">b(\cdot\mid\sfS)</script><span>得到</span></p><h3 id='改为-43'><span>改为</span></h3><p><span>2.3.1（执行）用行为策略</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.218ex" height="2.577ex" viewBox="0 -806.1 1816 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="0" id="E192-MJMATHI-62" d="M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z"></path><path stroke-width="0" id="E192-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path stroke-width="0" id="E192-MJSSI-53" d="M161 478Q161 568 242 642T435 716Q527 716 599 673L609 667Q595 633 589 615L571 568Q570 568 564 575T546 592T518 611T475 628T417 635Q351 635 305 596T259 507Q259 465 290 444T372 411T432 396Q473 385 509 343T545 236Q545 140 464 59T270 -22Q155 -22 54 48L92 146Q93 146 101 138T124 117T161 92T216 72T288 63Q360 63 403 109T447 204Q447 220 444 233T435 256T421 273T404 285T385 295T366 301T347 306T331 310T315 314T292 321T265 331T235 346T207 367T183 395T168 431T161 478Z"></path><path stroke-width="0" id="E192-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E192-MJMATHI-62" x="0" y="0"></use><use xlink:href="#E192-MJMAIN-28" x="429" y="0"></use><use xlink:href="#E192-MJSSI-53" x="818" y="0"></use><use xlink:href="#E192-MJMAIN-29" x="1427" y="0"></use></g></svg></span><script type="math/tex">b(\sfS)</script><span>得到</span></p><h2 id='第180页图9-1'><span>第180页图9-1</span></h2><h3 id='改为-44'><span>改为</span></h3><p><img src="./images/figure09_01.png" style="width: 200px;"/></p><h2 id='第180页第4行'><span>第180页第4行</span></h2><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.979ex" height="1.877ex" viewBox="0 -755.9 852 808.1" role="img" focusable="false" style="vertical-align: -0.121ex;"><defs><path stroke-width="0" id="E195-MJMATHI-58" d="M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E195-MJMATHI-58" x="0" y="0"></use></g></svg></span><script type="math/tex">X</script><span>轴是水平向下的，</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.772ex" height="1.877ex" viewBox="0 -755.9 763 808.1" role="img" focusable="false" style="vertical-align: 0.002ex; margin-bottom: -0.124ex;"><defs><path stroke-width="0" id="E196-MJMATHI-59" d="M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E196-MJMATHI-59" x="0" y="0"></use></g></svg></span><script type="math/tex">Y</script><span>轴是水平向右的。</span></p><h3 id='改为-45'><span>改为</span></h3><p><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.979ex" height="1.877ex" viewBox="0 -755.9 852 808.1" role="img" focusable="false" style="vertical-align: -0.121ex;"><defs><path stroke-width="0" id="E195-MJMATHI-58" d="M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 212 683H226Q260 681 347 681Q380 681 408 681T453 682T473 682Q490 682 490 671Q490 670 488 658Q484 643 481 640T465 637Q434 634 411 620L488 426L541 485Q646 598 646 610Q646 628 622 635Q617 635 609 637Q594 637 594 648Q594 650 596 664Q600 677 606 683H618Q619 683 643 683T697 681T738 680Q828 680 837 683H845Q852 676 852 672Q850 647 840 637H824Q790 636 763 628T722 611T698 593L687 584Q687 585 592 480L505 384Q505 383 536 304T601 142T638 56Q648 47 699 46Q734 46 734 37Q734 35 732 23Q728 7 725 4T711 1Q708 1 678 1T589 2Q528 2 496 2T461 1Q444 1 444 10Q444 11 446 25Q448 35 450 39T455 44T464 46T480 47T506 54Q523 62 523 64Q522 64 476 181L429 299Q241 95 236 84Q232 76 232 72Q232 53 261 47Q262 47 267 47T273 46Q276 46 277 46T280 45T283 42T284 35Q284 26 282 19Q279 6 276 4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E195-MJMATHI-58" x="0" y="0"></use></g></svg></span><script type="math/tex">X</script><span>轴是水平向上的，</span><span class="MathJax_SVG" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.772ex" height="1.877ex" viewBox="0 -755.9 763 808.1" role="img" focusable="false" style="vertical-align: 0.002ex; margin-bottom: -0.124ex;"><defs><path stroke-width="0" id="E196-MJMATHI-59" d="M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#E196-MJMATHI-59" x="0" y="0"></use></g></svg></span><script type="math/tex">Y</script><span>轴是水平向左的。</span></p><h2 id='第191页表10-1共4处）'><span>第191页表10-1（共4处）</span></h2><p><span>NoFrameSkip</span></p><h3 id='改为-46'><span>改为</span></h3><p><span>NoFrameskip</span></p><h2 id='第207页图11-3'><span>第207页图11-3</span></h2><h3 id='改为-47'><span>改为</span></h3><p><img src="./images/figure11_03.png" style="width: 400px;"/></p></div></div>
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